Dynamic construction of an antidictionary with linear complexity

Ota, Tetsuji; Fukae, Hirotada; Morita, Hiroyuki

doi:10.1016/j.tcs.2014.01.021

Cited by 5 publications

(1 citation statement)

References 18 publications

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“…In this paper, we study the following classes of strings in the sliding window model: Minimal Unique Substrings (MUSs) and Minimal Absent Words (MAWs). MUSs have been heavily utilized for solving the Shortest Unique Substring (SUS ) problem [10,13,6,8], and MAWs have applications to data compression based on anti-dictionaries [3,9]. However, despite the fact that there is a common application field to MUSs and MAWs such as bioinformatics [5,10,1,12], to our knowledge, these two objects were considered to be quite different and were studied separately.…”

Section: Introductionmentioning

confidence: 99%

Minimal Unique Substrings and Minimal Absent Words in a Sliding Window

Mieno

Kuhara

Akagı

et al. 2020

SOFSEM 2020: Theory and Practice of Computer Science

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A substring u of a string T is called a minimal unique substring (MUS) of T if u occurs exactly once in T and any proper substring of u occurs at least twice in T . A string w is called a minimal absent word (MAW) of T if w does not occur in T and any proper substring of w occurs in T . In this paper, we study the problems of computing MUSs and MAWs in a sliding window over a given string T . We first show how the set of MUSs can change in a sliding window over T , and present an O(n log σ)-time and O(d)-space algorithm to compute MUSs in a sliding window of width d over T , where σ is the maximum number of distinct characters in every window. We then give tight upper and lower bounds on the maximum number of changes in the set of MAWs in a sliding window over T . Our bounds improve on the previous results in [Crochemore et al., 2017].

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Section: Introductionmentioning

confidence: 99%

Minimal Unique Substrings and Minimal Absent Words in a Sliding Window

Mieno

Kuhara

Akagı

et al. 2020

SOFSEM 2020: Theory and Practice of Computer Science

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Minimal Absent Words in a Sliding Window and Applications to On-Line Pattern Matching

Crochemore

Héliou

Kucherov

et al. 2017

Fundamentals of Computation Theory

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International audienceAn absent (or forbidden) word of a word y is a word that does not occur in y. It is then called minimal if all its proper factors occur in y. There exist linear-time and linear-space algorithms for computing all minimal absent words of y (Crochemore et al. in Inf Process Lett 67:111–117, 1998; Belazzougui et al. in ESA 8125:133–144, 2013; Barton et al. in BMC Bioinform 15:388, 2014). Minimal absent words are used for data compression (Crochemore et al. in Proc IEEE 88:1756–1768, 2000, Ota and Morita in Theoret Comput Sci 526:108–119, 2014) and for alignment-free sequence comparison by utilizing a metric based on minimal absent words (Chairungsee and Crochemore in Theoret Comput Sci 450:109–116, 2012). They are also used in molecular biology; for instance, three minimal absent words of the human genome were found to play a functional role in a coding region in Ebola virus genomes (Silva et al. in Bioinformatics 31:2421–2425, 2015). In this article we introduce a new application of minimal absent words for on-line pattern matching. Specifically, we present an algorithm that, given a pattern x and a text y, computes the distance between x and every window of size |x| on y. The running time is O(σ|y|)O(σ|y|) , where σσ is the size of the alphabet. Along the way, we show an O(σ|y|)O(σ|y|) -time and O(σ|x|)O(σ|x|) -space algorithm to compute the minimal absent words of every window of size |x| on y, together with some new combinatorial insight on minimal absent words

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Absent words in a sliding window with applications

Crochemore¹,

Héliou²,

Kucherov³

et al. 2020

Information and Computation

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An absent word of a word y is a word that does not occur in y. It is then called minimal if all its proper factors occur in y. In fact, minimal absent words (MAWs) provide useful information about y and thus have several applications. In this paper, we propose an algorithm that maintains the set of MAWs of a fixed-length window sliding over y online. Our algorithm represents MAWs through nodes of the suffix tree. Specifically, the suffix tree of the sliding window is maintained using modified Senft's algorithm (Senft, 2005), itself generalizing Ukkonen's online algorithm (Ukkonen, 1995). We then apply this algorithm to the approximate pattern-matching problem under the Length Weighted Index distance (Chairungsee and Crochemore, 2012). This results in an online O(σ |y|)-time algorithm for finding approximate occurrences of a word x in y, |x| ≤ |y|, where σ is the alphabet size.

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Dynamic construction of an antidictionary with linear complexity

Cited by 5 publications

References 18 publications

Minimal Unique Substrings and Minimal Absent Words in a Sliding Window

Minimal Unique Substrings and Minimal Absent Words in a Sliding Window

Minimal Absent Words in a Sliding Window and Applications to On-Line Pattern Matching

Absent words in a sliding window with applications

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